Application of the Thermodynamic Extremal Principle to Massive Transformations in Fe-C Alloys
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DIFFUSION-CONTROLLED phase transformations such as austenite-ferrite (c-a) transformations have been studied extensively because of their importance in determining the microstructures, composition distributions and stability of retained austenite in steels.[1–4] A special massive transformation (MT) mode with a high growth velocity and negligible composition difference between the parent and the product phase was paid much attention.[5,6] MT was initially considered to be consistent with the interface-controlled transformation model of Christian[7] but inconsistent with the diffusion-controlled transformation model of Zener.[8] In fact, an extremely thin spike, which significantly influences phase-transformation kinetics, was always considered to be formed ahead of the migrating interface in MT.[9,10] Because its
XIN LI, WANGWANG KUANG, JIANBAO ZHANG, QING ZHOU, and HAIFENG WANG are with the State Key Laboratory of Solidification Processing, Center of Advanced Lubrication and Seal Materials, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P.R. China. Contact e-mails: [email protected]; [email protected] Manuscript submitted April 23, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS A
thickness is smaller than the atomic spacing according to the model calculations in substitutional alloys,[1,11,12] the existence of such spike is still in dispute. Considering that the solute diffusivity of C is much larger than that of the substitutional elements, the thickness of the spike in Fe-C alloys should be much larger, thus providing a chance to show the existence of the spike in MT. Liu et al.[13,14] carried out the pioneering work on the transition from diffusive transformation (DT) to MT in ultra-low-carbon Fe-C alloys and found that MT could be initiated in the two-phase region. Furthermore, the nucleation, growth and impingement kinetics of MT[9] were described by a modular approach in which the interface-controlled growth mode with negligible solute diffusion near the interface was adopted.[15] Up to now, several models have been proposed to describe the c fi a phase transformations. In the commercial software DICTRA,[16] a local equilibrium condition is assumed at the interface, and the phase transformation is controlled by bulk diffusion, i.e., the local equilibrium model (denoted as Model II in the current work). v C;eq Fe C lC JC xc xC;eq : lFe a ¼ lc ; a ¼ lc ; c ¼ a Vm ½1
Here, lip is the chemical potential of component i in C;eq the pð¼ a; cÞ phase. JC are the flux and the p and xp equilibrium mole fraction of C. v is the growth velocity, and Vm is the mole volume. The superscript ‘‘*’’ denotes the variables at the interface. Regarding the nature of the mixed-growth mode in practical phase transformations, a mixed-mode model with finite mobility was proposed by Sietsma and Zwaag[17] in which interface migration and solute diffusion in bulk phase were considered simultaneously: xC v ¼ MDG ¼ Mv xC;eq ; c c ½2 v C C C;eq xc xa : Jc ¼ Vm Here M is the mobility of interfa
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